[MH] Rapid Fire, Average Damage and DR

[SCAR]

Monster Hunters 2.p21 suggests using Average Damage for 4+ hits, primarily to save time. This seems like a good idea, (and is not the first time it has been suggested). There is however a small mathematical problem, when the targets DR exceeds average damage but is below maximum damage. In these cases, using average damage means the attack cannot cause any injury even though the attack is capable of exceeding DR and causing damage.

For example: A shotgun with 1d6+1 damage and RoF 3x9 (27 pellets) with a Rcl of 1, attacking a DR5 monster.
With a sufficiently high skill and bonuses, an attack might hit with a dozen or more pellets. Average damage is 4.5, which against DR5 will result in no damage.
Mathematically, on average 2 in 6 hits are capable of causing damage; a roll of 5 or 6 (+1) will cause 1 and 2 points of damage respectively; which for 12 hits would equate (on average) to 6 points of damage.

If this were just 1 or 2 points of damage, it wouldn’t really be worth worrying about, but with high RoF weapons (including Shotguns), and possibly experimental UT weapons, 10+ hits with a mathematical average damage of 1+ is sufficient damage to be worth worrying about, especially for desperate Hunters facing tough Monsters that their weapons can only just scratch!

However, since the point of using average damage is to save time, we don’t want to add lots more complexity as that would defeat the whole point. Fortunately MH2 gives us the hook we need (pre-calculating damage, again to save time), and a bit of maths gives us what we need – short reference tables of average damage.

The tables are in the next 2 posts if you want to skip straight to them without the maths heavy explanation!

How it Works!

The starting point is quite simple, and is the same as the standard Average Damage mechanic:

For DR less than Half of Maximum Damage: Average Damage for the Weapon – Target DR;

Damage should be treated as just the Nd, ‘adds’ should be subtracted directly from DR; for example: 1d+1 vs. DR5 becomes 1d vs. DR4; and 2d-1 vs. DR6 becomes 2d vs. DR7. Any armor divisors should be applied to the targets DR before adjusting for any ‘adds’.

For 1D6: Average (DR0) = 3.5; DR1 = 2.5; DR2 = 1.5; (DR3 is half maximum damage of 6 so we stop there at this stage).
For 2D6: Average (DR0) = 7; DR 1 = 6; ..; DR5 = 2; (DR6 is half maximum damage of 12 so we stop there at this stage).

When DR reaches half of maximum damage, Average Damage steps down in increments of 0.5 for each additional +1 DR until we get to an Average Damage of 0.5.

For 1D6: Average (DR2) was 1.5; so DR3 = 1.0 (instead of 0.5); and DR4 = 0.5;
For 2D6: Average (DR5) was 2.0; so DR6 = 1.5; DR7 = 1.0; and DR8 = 0.5;

The additional trick to making this work is to apply a Minimum Number of Hits to get this Modified Average Damage. The Minimum Number of hits is based on the probabilities of getting a damage roll which can penetrate DR. For 1D6 vs. DR3 a roll of 4-6 will inflict damage which is half the rolls, so Minimum is 2 hits; similarly for 1D6 vs. DR4 a roll of 5 or 6 will inflict damage, which is a third of the rolls, so Minimum is 3 hits.
Fortunately this becomes even easier; the Minimum Number of Hits for the Modified Average Damage is 4 or less in all but 2 cases up to 6D6; since we’re only using ‘Average Dice’ for 4+ Hits we can skip this Min Hits check.
(The exceptions are 5D6 vs. DR20, and 6D6 vs. DR24, both of which have a modified average damage of 0.5, and a minimum number of hits of 5 – close enough to ignore the Minimum Number of Hits in these 2 cases I think!)

If we can ignore Minimum Number of Hits, why bring it up I hear you ask; because it is relevant for the final step – where average damage is below 0.5. For these we build simple lookup tables.
Note: Some of the results are quite extreme with regards minimum number of hits, especially for 3D6 or more, and DR close to maximum damage – for example; 4D6 vs. DR22 gets 1 point of damage for every 259 hits! These entries are listed for completeness rather than usefulness – even for weapons with very high RoF!

[SCAR]

Each table is for a number of D6 damage (From 1 to 6), listing Average Damage per Hit for a targets DR from 0 to Maximum Damage -1 (i.e. the maximum DR which the attack can still penetrate).

Any Armor Divisor should be applied to the DR first; and then any ‘Adds’ on the damage should be subtracted from the remaining DR. (‘subtracts’ on the damage should be added to the DR!)

Then lookup the final DR on the table for the base damage dice to get the Average Damage per Hit, and were required, the Minimum Number of Hits required to score any damage.

Note: For High DRs, the Minimum Number of Hits is the per N value, i.e. 3D6 vs. DR17, Average Damage in 1 per 216, Minimum Number of Hits is also 216.

These tables can be used for a quick look up as a replacement for simply recording and using the Basic Average Damage for a Weapon. Write them on a card index, or record them on your character sheet along with the other pre-calculated attack/weapons stats.

TABLES - Part 1:

1D6  DR   Avg.Dmg
      0     3.5
      1     2.5
      2     1.5
      3     1.0     (Min 2 hits)
      4     0.5     (Min 3 hits)
      5    1 per 6  (Min 6 hits)

2D6  DR   Avg.Dmg
      0	    7.0
   1 to 4   7.0-DR
      5     2.0
      6     1.5     (Min 2 hits)
      7     1.0     (Min 2 hits)
      8     0.5     (Min 3 hits)
      9    1 per 4  (Min 6 hits)
      10   1 per 9  (Min 12 hits)
      11   1 per 36 

3D6  DR   Avg.Dmg
      0    10.5
   1 to 7  10.5-DR
      8     2.5
      9     2.0     (Min 2 hits)
     10     1.5     (Min 2 hits)
     11     1.0     (Min 2 hits)
     12     0.5     (Min 4 hits)
     13    1 per 3  (Min 6 hits)
     14    1 per 6  (Min 11 hits)
     15    1 per 14 (Min 22 hits)
     16    1 per 50 (Min 54 hits)
     17    1 per 216

[SCAR]

TABLES - Part 2:

4D6  DR   Avg.Dmg
      0    14.0
   1 to 10 14.0-DR
     11    3.0
     12    2.5      (Min 2 hits)
     13    2.0      (Min 2 hits)
     14    1.5      (Min 2 hits)
     15    1.0      (Min 3 hits)
     16    0.5      (Min 4 hits)
     17   1 per 3   (Min 6 hits)
     18   1 per 5   (Min 10 hits)
     19   1 per 10  (Min 19 hits)
     20   1 per 25  (Min 37 hits)
     21   1 per 50  (Min 86 hits)
     22   1 per 259
     23   1 per 1296

5D6  DR   Avg.Dmg
      0    17.5
   1 to 13 17.5-DR
     14    3.5
     15    3.0      (Min 1 hits)
     16    2.5      (Min 2 hits)
     17    2.0      (Min 2 hits)
     18    1.5      (Min 3 hits)
     19    1.0      (Min 3 hits)
     20    0.5      (Min 5 hits)
     21   1 per 3   (Min 7 hits)
     22   1 per 5   (Min 10 hits)
     23   1 per 8   (Min 17 hits)
     24   1 per 17  (Min 31 hits)
     25   1 per 33  (Min 62 hits)
     26   1 per 100 (Min 139 hits)
     27   1 per 370
     28   1 per 1296
     29   1 per 7776

6D6  DR   Avg.Dmg
      0    21.0
   1 to 16 21.0-DR
     17    4.0
     18    3.5      (Min 1 hits)
     19    3.0      (Min 2 hits)
     20    2.5      (Min 2 hits)
     21    2.0      (Min 2 hits)
     22    1.5      (Min 3 hits)
     23    1.0      (Min 4 hits)
     24    0.5      (Min 5 hits)
     25   1 per 3   (Min 7 hits)
     26   1 per 4   (Min 10 hits)
     27   1 per 7   (Min 17 hits)
     28   1 per 14  (Min 28 hits)
     29   1 per 25  (Min 51 hits)
     30   1 per 50  (Min 101 hits)
     31   1 per 100 (Min 222 hits)
     32   1 per 555
     33   1 per 1666
     34   1 per 6665
     35   1 per 46656

[SCAR]

Some Examples:

Auto shotgun [M1.p62] 1d+1pi; RoF3x9; Rcl1 - 10 hits vs. DR4:

The +1 damage comes directly off the DR leaving DR3
From the 1D6 table, DR3 has Average Damage 1.0 per hit, Min 2 hits (OK)
Total is 10 points of damage (1.0x10 = 10)
The pi damage type has a x1 modifier (assuming no specific hit location or injury tolerance modifiers)

SMG, 9mm [M1.p62] 3d-1pi; RoF13; Rcl2 - 7 hits vs. DR12:

The -1 damage adds directly to DR giving DR13
From the 3D6 table, DR13 has Average Damage 1 per 3, Min 6 hits (OK)
Total is 2 points of damage (7 / 3 = 2 x 1 = 2);

5 hits would have been below the Minimum Number of Hits, and would have resulted in No damage.

For 11 hits vs. DR13:
The -1 damage adds directly to DR giving DR14
From the 3D6 table, DR14 has Average Damage 1 per 6, Min 11 hits (Just enough)
Total is 1 points of damage (11 / 6 = 1 x 1 = 1). (12 hits would have been 2 points of damage);

Assault Carbine [M1.p62] 4d+2pi; RoF15; Rcl2 - 5 hits vs. DR12:

The +2 damage subtracts from the DR giving DR10
From the 4D6 table, DR10 has Average Damage 14.0-DR = 4 (the same as the standard Average Dice calculation would have given)
Total is 20 damage (4 x 5 = 20)

[weby]

Actually the opposite problem is worse, an armor rated to stop a given attack normally stops it very reliably, the rolled damage range being so large makes armor ineffective, thus using the average damage is a better solution even for single hits, than the rolled damage.

[SCAR]

Originally Posted by weby

Actually the opposite problem is worse, an armor rated to stop a given attack normally stops it very reliably, the rolled damage range being so large makes armor ineffective, thus using the average damage is a better solution even for single hits, than the rolled damage.

It depends upon whether you have the gun or the armor - since these rules are primarily for Monster Hunters attacking Monsters, I can see players being very keen on even a slim chance of injuring something beyond average damage, especially if you're using very high RoF weapons.

"Perhaps a clip from your autopistol can't hurt it, but how about a couple of hundred rounds from my minigun?"

For example 100 hits for a 1D6 weapon vs. DF5 and you get zero damage, some people will not like that!

[Bruno]

Originally Posted by SCAR

It depends upon whether you have the gun or the armor - since these rules are primarily for Monster Hunters attacking Monsters, I can see players being very keen on even a slim chance of injuring something beyond average damage, especially if you're using very high RoF weapons.

This also assumes that monsters aren't using guns - in my experience most monsters with hands and IQ 8 or higher will be as likely to use guns as PCs are (especially when you consider some of the PCs are monsters).

Particularly high on my list of monsters-that-use-guns are vampires (who, after all, were humans once and are smart enough not to toussle with Crusaders in hand-to-hand combat) and witches (who ARE humans, and have a difficult time with quick blast spells as good as gunfire ;)

Originally Posted by SCAR

For example 100 hits for a 1D6 weapon vs. DF5 and you get zero damage, some people will not like that!

My first inclination is to answer the "some people" with "You obviously don't want to be playing in a rules light game."

More lookup tables is the opposite of fast and rules-light. I'd rather just use a macro, because then there's NO math, just a number spat out.

[SCAR]

Originally Posted by Bruno

This also assumes that monsters aren't using guns - in my experience most monsters with hands and IQ 8 or higher will be as likely to use guns as PCs are (especially when you consider some of the PCs are monsters).

Particularly high on my list of monsters-that-use-guns are vampires (who, after all, were humans once and are smart enough not to toussle with Crusaders in hand-to-hand combat) and witches (who ARE humans, and have a difficult time with quick blast spells as good as gunfire ;)

And since the PCs are the Hero's, the Monsters will likely use the standard Average Damage to favor the PCs.

I might well use the standard Average Damage rules under most circumstances, but there would be times when a quick table lookup (as opposed to (Average Damage minus DR) calculation, not really any slower!) for the chance would be useful.

Originally Posted by Bruno

My first inclination is to answer the "some people" with "You obviously don't want to be playing in a rules light game."

It doesn't have to be rules light; Quick play is the point - and it isn't restricted to Monster Hunters. A gritty realistic game might still want fast play.

I personally don't want to play gun combat to the sort of realistic detail covered by Tactical Shooting, that doesn't mean I won't buy it and pilfer the odd idea from it which does suit my style of play.

You also run into the possibility of higher skill PCs only firing 3 shots, knowing they will likely hit with them all, so they can Roll Damage for the chance of a hit, rather than get 4+ hits and Average Damage. For example, a 1D6 weapons with RoF 10, vs DR4. If you have a chance of 4 or 5 hits, Average Damage will give you 2 points of damage; Rolling 3 hits will give you (on average) 3 points of damage - which the above quick tables would also give, and they would give 4 or 5 points of damage for the 4 or 5 hits - and all with no more time or effort than the existing Average Damage calculation!

Originally Posted by Bruno

More lookup tables is the opposite of fast and rules-light. I'd rather just use a macro, because then there's NO math, just a number spat out.

Using a Macro isn't really a fair comparison, nor is it useful at a gaming table with no 'computers'. Even with a 'computer' at the table (and not full online gaming), you might have to enter or select the particular character/weapon/target to get the right Damage, DR etc for the calculations.

[Bruno]

Originally Posted by SCAR

And since the PCs are the Hero's, the Monsters will likely use the standard Average Damage to favor the PCs.

I might well use the standard Average Damage rules under most circumstances, but there would be times when a quick table lookup (as opposed to (Average Damage minus DR) calculation, not really any slower!) for the chance would be useful.

Average Damage Go Find The Table Cross Reference isn't any simpler, and apparently is intended to produce lopsided results.

I'm confused as to your goals with it, and the results (lopsided) seem to be a fundementally bad idea. Creating different rules depending on whether you're a PC or NPC results in players getting really confused as to what the rules are, and that's never good.

Originally Posted by SCAR

It doesn't have to be rules light; Quick play is the point - and it isn't restricted to Monster Hunters. A gritty realistic game might still want fast play.

Quick play is rules light - they're synonymous. It has nothing to do with grit and realism, that's a separate thing entirely and has nothing to do with your table.

Originally Posted by SCAR

You also run into the possibility of higher skill PCs only firing 3 shots, knowing they will likely hit with them all, so they can Roll Damage for the chance of a hit, rather than get 4+ hits and Average Damage. For example, a 1D6 weapons with RoF 10, vs DR4. If you have a chance of 4 or 5 hits, Average Damage will give you 2 points of damage; Rolling 3 hits will give you (on average) 3 points of damage - which the above quick tables would also give, and they would give 4 or 5 points of damage for the 4 or 5 hits - and all with no more time or effort than the existing Average Damage calculation!

Except that table lookups are more time and effort than writing down average damage?

Originally Posted by SCAR

Using a Macro isn't really a fair comparison, nor is it useful at a gaming table with no 'computers'.

I don't see why it's "unfair" - some gaming areas have computers, some don't have space for extra tables clipped to things. Both are situational, so I really can't see how a macro is "cheating".

I'm also not sure why there are suddenly quotes around "computer". It's not an alleged computer, it's a computer.

Originally Posted by SCAR

Even with a 'computer' at the table (and not full online gaming), you might have to enter or select the particular character/weapon/target to get the right Damage, DR etc for the calculations.

Having to put in (or select from saved presets) 5d+6 and DR 12 is just like having to cross reference your tables. Only with less lines to get mixed up in.

[Crakkerjakk]

Originally Posted by Bruno

I'm also not sure why there are suddenly quotes around "computer". It's not an alleged computer, it's a computer.

Snrk.

I say switch over to armor as dice. Simplest way I've seen for armor to stop what it's supposed to and still keep variable damage. Though for rapidfire hits I've always just rolled damage once and then multiplied it by the number of hits. May not be the most realistic, but over time the results of rolling a single high or low damage hit and getting it multiplied across several hits average out, and it saves a lot of time.